Promoting your app is one of the most important things you must do after relasing it, for some developers it's harder and for other it's easier;
More skilled and famous developers get automatically promoted by news websites as soon as they release an app, giving them an instant boost in downloads, unfortunatelly for us little developers we have to rely on out own strenghts.

There are a lot of ways to advertise your apps, some are free and for others you'll have to invest some money, some ways are better and some others are worse.

Free advertising:

Social networks:
The first thing that will come in mind for promoting an app is thru social networks, sharing the link for the play store with friends and other people is the best way to start, if someone likes your post they'll share it with others making it a viral spread of your word and your app

If you're a good developer and you make great apps it won't be difficult for people to talk about it

YouTube
Another great platform for advertising is YouTube, watching a short video is way better than reading something, and as always if it's enjoyable it will be shared by people.

2. Making a commercial video showing what your app can do, it's strenghts and why people should downlaod it, i didn't make one yet so i don't have anything to show you unfortunatelly

Make it good
The most obvious, make the app good, look at your competition, make the app better than their.
Something i see a lot in Android apps it the awful UI, the UI is the first thing people see, even before installing it, they can see the screenshorts of your app, and they decide if they want to install it or not.

Making a nice UI is important as the coding, if you're not a designer and can't do it hire one, there's a plenty of graphic designers willing to make a quick buck, maybe in exchange you can advertise his work, you can also contact me and we can arrange something.

Ways to attract users
Another great thing to do to attract users is to make some nice ads, spend a little time in photoshop and make some good feature and promo graphics for the play store, also when posting it in social networks etc. use those graphics, they'll attract more people than just plain text with a link
Here are some examples for my app Wakey
Feature:

AD

Get your app reviewed
One of the best ways to get your app promoted for free is to get it reviewed by an Android news website, when i got my app reviewed on XDA it went from 3-5 downloads a day to 300 a day

Partnerships
When i released Wakey i've been contacted by the writer of geekshavelanded.com and he gave me the opportunity to promote my app even further, i've put a link to his website in my app and he've put a little ad for Wakey in the sidebar, this way i get more downlaods and he gets his website promoted aswell

Discounts
If your app is paid or have in app purchases, a nice way to get noticed it's to make some discounts, usually on major holidays like easter, christmas etc, a lot of developers make discounts and a lot of websites post a list of discounted apps during that period of time

Other
There are also other ways to promote your apps, like i'm doing right now, by writing this guide i'm promoting my app Wakey, i'm using it as a reference for this article so when you see the links, the graphics, you view them because you'd like to learn about promoting your apps and not because i'm imposing you to do so.
So hopefully i'll gain some downloads and purchases by doing so, also you'll be supporting my development (see what i did there ? )

Paid advertising

Web ads
There are plenty of advertising services out there, like AdMob or AdSense, you can use those to promote your apps on different websites.
Another way is to contact a single website and talk about placing a custom banner on their website

Giveaways
This is a very simple but effective form of advertising, who doesn't want something for free?
You can post an article or a post on a social network about the giveaway (you can giveaway all sorts of things, from t shirts to smartphones etc.) people will be more interested in buying/downloading your app if they know they might win something

Printing
You can print some business cards and give them to people you encounter, also if you have a bigger budget you can print some billboards

TV/Radio commercials
Very effective way but also very expensive, but for bigger developers it might be a good solution

As i said there are a lot of possibilities, some more and some less effective, it's up to you choosing which one is the best for you, your app and your audience

You can follow me on G+ or YouTube where i will be posting some tutorials on android app design

I need to do some more research into what those feature and promo images in the dev console actually do. There wasn't much information there so I just left them blank. But I see how they may be useful.

I need to do some more research into what those feature and promo images in the dev console actually do. There wasn't much information there so I just left them blank. But I see how they may be useful.

Here's a little image to explain it, the feature image is the one shown on the page of your app, the promo image is the one shown when your app is chosen by google as "Staff pick"

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